Question

A question regarding "equality" of word lengths for two minimal generating sets of a finite group

score 20 · Answer 1 · 2026-03-25 19:06:48

20

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A question regarding "equality" of word lengths for two minimal generating sets of a finite group

Published on 25 Mar 2026 - 19:06

score 155 · Answer 2 · 2019-05-26 17:59:39

155

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How to check the property of projective linear group

Published on 26 May 2019 - 17:59

score 102 · Answer 3 · 2026-03-26 22:52:30

102

Views

Can $A_n$ be generated by two elements $x,y$ with $x\ne 1$ arbitrarily chosen?

Published on 26 Mar 2026 - 22:52

score 91 · Answer 4 · 2026-03-26 22:58:20

91

Views

Show that if $G \leq S_{n} $ has $r$ orbits when acting on $ \{ 1 , \dots , n \} $, then it is generated by at most $n - r $ elements.

Published on 26 Mar 2026 - 22:58

score 205 · Answer 5 · 2019-05-27 11:59:25

205

Views

The Orbit-Stabilizer Theorem: any information on stabilizers' mutual inclusion/intersection?

Published on 27 May 2019 - 11:59

score 264 · Answer 6 · 2026-03-26 22:57:58

264

Views

Example of exotic $S_5$ as a Galois group

Published on 26 Mar 2026 - 22:57

score 1.1k · Answer 7 · 2019-05-27 17:04:15

1.1k

Views

Finite non-Abelian group $|G| = pq$, $p>q$ primes, prove: $q\ |\ p-1$

Published on 27 May 2019 - 17:04

score 86 · Answer 8 · 2026-03-29 07:19:52

86

Views

Sizes of conjugacy classes in $\mathrm{GL}_n(\mathbb{F}_q)$

Published on 29 Mar 2026 - 7:19

score 464 · Answer 9 · 2026-03-30 20:44:17

464

Views

$G$ is a non-abelian group of order 6 $ \implies G \approx S_3 $. Simpler proof?

Published on 30 Mar 2026 - 20:44

score 110 · Answer 10 · 2026-03-26 01:03:37

110

Views

A finitely generated abelian group $G$ has an element of order $\exp(G)$

Published on 26 Mar 2026 - 1:03

score 81 · Answer 11 · 2026-03-25 04:57:31

81

Views

What do we learn about a non-abelian simple group from the numbers "inside" its character table?

Published on 25 Mar 2026 - 4:57

score 743 · Answer 12 · 2019-05-30 14:20:42

743

Views

Group actions, the Orbit-Stabilizer Theorem and Burnside's Lemma.

Published on 30 May 2019 - 14:20

score 183 · Answer 13 · 2026-03-27 23:57:36

183

Views

Cyclic groups, generators, quotient groups

Published on 27 Mar 2026 - 23:57

score 200 · Answer 14 · 2019-05-30 17:25:44

200

Views

How many group homomorphisms $g: \mathbb{Z}_{5} \oplus \mathbb{Z}_{10} \to \mathbb{Z}_{15}$ are there?

Published on 30 May 2019 - 17:25

score 203 · Answer 15 · 2019-05-30 18:11:08

203

Views

Is it true that an abelian group is cyclic iff every $n$-torsion subgroup is cyclic?

Published on 30 May 2019 - 18:11

List Question

A question regarding "equality" of word lengths for two minimal generating sets of a finite group

How to check the property of projective linear group

Can $A_n$ be generated by two elements $x,y$ with $x\ne 1$ arbitrarily chosen?

Show that if $G \leq S_{n} $ has $r$ orbits when acting on $ \{ 1 , \dots , n \} $, then it is generated by at most $n - r $ elements.

The Orbit-Stabilizer Theorem: any information on stabilizers' mutual inclusion/intersection?

Example of exotic $S_5$ as a Galois group

Finite non-Abelian group $|G| = pq$, $p>q$ primes, prove: $q\ |\ p-1$

Sizes of conjugacy classes in $\mathrm{GL}_n(\mathbb{F}_q)$

$G$ is a non-abelian group of order 6 $ \implies G \approx S_3 $. Simpler proof?

A finitely generated abelian group $G$ has an element of order $\exp(G)$

What do we learn about a non-abelian simple group from the numbers "inside" its character table?

Group actions, the Orbit-Stabilizer Theorem and Burnside's Lemma.

Cyclic groups, generators, quotient groups

How many group homomorphisms $g: \mathbb{Z}_{5} \oplus \mathbb{Z}_{10} \to \mathbb{Z}_{15}$ are there?

Is it true that an abelian group is cyclic iff every $n$-torsion subgroup is cyclic?

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